In Exercises 31 and 32, find an equation for (a) the tangent to the curve at P and (b) the horizontal tangent to the curve at Q. 31. 32. 5, 2 1 4 P # 4 x 2 O y =4+ cot.x - 2csc x 0 y =1 +12 csc x + cotx 42. Use the identity sin 2x = 2 sin x cos x to find the derivative of sin 2x. Then use the identity cos 2x = cos2 x - sing x to express that derivative in terms of cos 2x. 43. Use the identity cos 2x = cos x cos x - sin x sin x to find the derivative of cos 2x. Express the derivative in terms of sin 2r. 1999 725 38. Find da 999 (cos x ). 39. Find dx 725 (sin x)